Simple Interest
Math MCQs

Question :    Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $11765 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $6500

Rate of Simple Interest (R) = 9% per annum

Amount (A) = $11765

Thus, time (T) = ?

Method (1) Using Formula

Calculation of Simple Interest, when Principal and Amount are given

Formual to Calculate Simple Interest when Principal and Amount are given

We know that, Amount (A) = Principal (P) + Simple Interest (SI)

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $11765 – $6500 = $5265

Thus, Simple Interest = $5265

Calculation of the Time using forumula when Amount, Simple Interest and Principal are known

Formula to find the Time (T)

Time (T) = ^{100 × Simple Interest}/_{Principal × Rate of Interest}

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 5265}/_{6500 × 9}

= ⁵²⁶⁵⁰⁰/₅₈₅₀₀

= 9 years (using formula)

Thus, Time (T) = 9 years (from time taken before calculation)Answer

Calculation of the Time using Unitary Method when Amount, Simple Interest and Principal are known

Here, we have

Principal (P) = $6500

Rate of Simple Interest (R) = 9% per annum

Simple Interest = $5265 (As calculated above by subtracting Principal from the Amount given)

We know that, interest is calculated on the basis of the Principal.

This means Simple Interest for 1 year = Rate of simple interest × Principal

Thus, Simple Interest for 1 year = 9% of Principal

= 9% of $6500

= ⁹/₁₀₀ × 6500

= ^{9 × 6500}/₁₀₀

= ⁵⁸⁵⁰⁰/₁₀₀ = 585

Thus, simple Interest for 1 year = $585

Now,

∵ If the simple Interest is $585, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₈₅ years

∴ If the simple Interest is $5265, then the time = ¹/₅₈₅ × 5265 years

= ^{1 × 5265}/₅₈₅ years

= ⁵²⁶⁵/₅₈₅ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $9500 to clear the loan, then find the time period of the loan.

(2) How much loan did Ryan borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9085 to clear it?

(3) Calculate the amount due if William borrowed a sum of $3500 at 2% simple interest for 3 years.

(4) What amount will be due after 2 years if James borrowed a sum of $3000 at a 6% simple interest?

(5) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 2% simple interest?

(6) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $11700 to clear the loan, then find the time period of the loan.

(7) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $8268 to clear the loan, then find the time period of the loan.

(8) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8970 to clear it?

(9) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $7548 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if Michael borrowed a sum of $3300 at 9% simple interest for 3 years.